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Put your satellite in perfect (or near perfect) synchronous orbit around Duna far away from Ike and it shouldn't be a problem.
It's like deploying relays around Kerbin when you want them so far apart but Ike will destroy anything that gets too close.
since the moon actually slows down the earth's rotation (very very slightly) it's possible that in some distant future the earth will also be tidally locked with the moon.
right now, an earth day would have to be slowed down to 1 month for that to happen - in that case the geostationary orbit would be (roughly) equivalent to the orbital distance of the moon. the moon would still "jump" up and down in the sky since it's orbital plane isn't perpendicular to the earth rotation axis.
Ah. Thanks for clarifying.